# Centripetal & centrifugal forces [duplicate]

If there are no centrifugal forces in reality then how to explain weight loss due to rotation of earth or dynamic balancing of a rotating mass?

The centrifugal force is one of the fictitious forces that lets one use Newton's laws in a domain (a non-inertial frame) in which they do not quite apply. There's always an explanation to Newtonian phenomena taken from the perspective of an inertial frame in which those fictitious forces do not exist. In some cases such as predicting the weather, using an inertial frame results in a numerical mess. The explanation from the perspective of an inertial frame still exists, but nobody uses it in the case of predicting the weather.

If there are no centrifugal forces in reality then how to explain weight loss due to rotation of earth or dynamic balancing of a rotating mass?

This is not one of those cases. The inertial explanation is easy. Consider a person of mass $m$ standing still at sea level at the equator. That person undergoes uniform circular motion at a radius $r$ of 6378 km from the center of the Earth and with an angular velocity $\omega$ of one revolution per sidereal day. This means the net force acting on that person must necessarily be non-zero. It is in fact $m r \omega^2$, directed toward the center of the Earth.

The only real forces acting on the person are the inward gravitational force, directed to the center of the Earth and the outward normal force, directed away from the center of the Earth. To yield a net inward force of $m r \omega^2$, the inward gravitational force (which can't be felt) must exceed the outward normal force (which can be felt) in magnitude by exactly this amount ($m r \omega^2$).

• This sentence is confusing "There's always an inertial frame answer to any question in which those fictitious forces appear to be essential." The phrase "inertial frame" is used as an adjective to the word "answer" but reads like the object of the sentence. I suggest to connect the words with hyphen as "inertial-frame-answer". – physicopath May 15 '18 at 15:04

The centrifugal force is a inertial force appearing in a rotating frame of reference. A fixed coordinate system on the surface of the earth is a rotating frame of reference. Thus a massive body on the surface of the earth experiences a centrifugal force leading to a reduction of its apparent weight which is strongest at the equator.

The earth, strictly speaking, is not an inertial frame of reference but it is quite a good approximation. Now coming back to your question, centrifugal force is a pseudo force which is assumed to be acting on every particle in an accelerated frame of reference. If the frame is accelerating with an acceleration a with respect to an inertial frame, then we apply a force -ma on each particle if we are working in the frame of reference of the accelerating frame. If the earth is rotating with respect to a fixed axis with an angular velocity w, then so is every particle on/inside earth with it. Thus if we are working from the earth frame of reference then we have to apply a force mw²r radially outward where r is the distance of the particle from the centre of the earth and m is it's mass. The net force on the particle decreases and hence the weight decreases.